On a picnic near the Provo River at Mt. Timpanogos park, just at the mouth of Provo Canyon, I spotted a new wild friend with easy identification: a Bullock's Oriole, a brilliant orange and black bird somewhat smaller than an American Robin and a cousin similar to the Baltimore Oriole of the east. He has a sharply defined black mask with a chin stripe that does not continue to his chest, and his vibrant color makes him easy to spot. This one was foraging in trees, nibbling off the leaf buds far above our heads, chattering randomly as he enjoyed his own picnic.
Spotting birds while walking trails is a great joy, but one that takes some practice in order to identify the wild wanderers. I would recommend going at a time when the light is good so any color variations in plumage are easily spotted, and try to get as close to the birds as possible so you can see details in their markings. Especially note the bill size and shape, head colorings, body size, wing markings, and rear view. If possible, also note what the bird is doing and any sounds you can clearly identify as coming from them.
When possible, snap a digital picture of the bird, one that you can zoom in on at a later date in order to compare the bird to books, field guides, websites, and other identification resources. Binoculars can also be a help, particularly for more reclusive species, if you have them available. My camera and zoom has helped me discover new species on several occasions, though with the clear and distinctive markings of the Bullock's Oriole, it wasn't necessary. I wouldn't recommend taking field guides with you while birding casually on a trail, since you'll waste valuable behavior observation time flipping through pages and making comparisons you can easily make after the bird has moved on.
With care and practice, you can easily find new and remarkable species no matter where you are, if you're prepared to observe them adequately. The best observation tools you have are your eyes, and with them, new birds can reveal a world you may never have known existed, a world that you share with many other intelligent and remarkable species.